A Model of Online Misinformation: Homophily and Reachability
A comment on Acemoglu, Ozdaglar, and Siderius (2024)
Abstract
Acemoglu, Ozdaglar, and Siderius (2024) show that greater homophily lowers engagement for sufficiently reliable content when each agent's expected degree is held fixed. In their high-reliability branch, every reached agent shares, so engagement equals expected network reach. A four-agent island network reverses the stated comparison. Under the expected-degree expression used in the proof, raising the within-island link probability from 9/10 to 99/100 and lowering the cross-island probability from 7/10 to 61/100 raises engagement from 0.983116 to 0.9864366. The reversal holds along a continuous fixed-degree family. The proof compares links between islands while the degree-preserving change also alters reach within each island. A replacement condition compares the pivotal reach of the two edge classes. At the reliability-one endpoint, full connectivity attains maximal engagement.
Technical point
Holding expected degree fixed does not sign the effect of homophily on reach; higher within-island connectivity can outweigh fewer cross-island links in the high-reliability all-share branch.
Scope
Claims affected
Theorem 2(b)'s high-reliability engagement comparison and the circulation interpretation attached to it.
What remains intact
Theorem 2(a) and the remaining range of Theorem 3(ii) lie outside the counterexample; at reliability one, a fully connected network still maximizes engagement.